Entropy of a quantum error correction code

Details Entropy of a quantum error correction code Entropy of a quantum error correction code

2008-11-11

arxiv.org/abs/0811.1621v1

Open Syst. Inf. Dyn. 15, 329-343 (2008).

Physics

Quantum Physics

13 pages, 1 figure, to appear in Open Systems & Information Dynamics

Scientific paper

We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme conditions and the entropy exchange computed with respect to any initial state supported on the code. In general the entropy of a code can be viewed as a measure of how close it is to the minimal entropy case, which is given by unitarily correctable codes (including decoherence-free subspaces), or the maximal entropy case, which from dynamical Choi matrix considerations corresponds to non-degenerate codes. We consider several examples, including a detailed analysis in the case of binary unitary channels, and we discuss an extension of the entropy to operator quantum error correcting subsystem codes.

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